Quandaries and Queries
  

 

I have to prove that the product of any n consecutive integers is divisible by n!(eg:the product of five consecutive integers is divisible by 5!) It's easy enough to plug in numbers and prove it is true, but i'm finding it difficult to come up with a proper proof. Can someone help me please?
 
Many Thanks
Fazia
(university mathematics student)
 

 

Let M be the largest of the n numbers.

  1. First ask yourself: In how many ways can you choose a n-member committee consisting of a president, a vice-president, a vice-vice-president (= vice2-president), ..., and a vice-vice-...-vice-president (= vicen-1-president) among M people.

  2. Then ask yourself: By how much should you divide that number to get the number of n-member committees chosen among M people, if the committee members have no title.

The answer to 2) is relevant to your question, but most importantly
it is an integer!

Claude

  
 

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